President Trump offers temporary protection for people brought to U.S. illegally as children in bid to secure border wall funding; Vice President Mike Pence breaks down the proposal on 'Fox News Sunday.'

Vice President Mike Pence, speaking to "Fox News Sunday," said Republicans "of course" remain willing to negotiate further on the border funding compromise proposed by President Trump on Saturday, even as Pence charged that House Speaker Nancy Pelosi has committed to a "disappointing" strategy of "soundbites" for nearly a month.

Pence's comments came as Fox News has learned that Senate Republicans were scrambling on Saturday evening and Sunday morning to put together a bill tracking Trump's proposal to end the ongoing partial federal government shutdown. Democratic leaders, including Pelosi, preemptively rejected Trump's proposal before he formally announced it.

Decrying the "obsession of many in the national media to attack this president for any reason, for any allegation," Pence asserted that the problem was bigger than BuzzFeed, which has stood by its reporting, without offering additional justification, despite Mueller's extraordinary rebuke.

Speaking to CNN later on Sunday, BuzzFeed reporter Anthony Cormier refused to explain why his co-writer on the bombshell story, Jason Leopold, had claimed in an interview to have seen documents verifying the story's claims -- even though Cormier, separately, said BuzzFeed had not seen the documents. "We can't get into, like, the details there," Cormier said Sunday, when pressed about the discrepancy.

"It was remarkable what we saw happening for 24 hours in the media, on the basis of the report that appeared in BuzzFeed," Pence told anchor Chris Wallace. "It's one of the reasons why people are so frustrated with many in the national media."

But, speaking later to "Fox News Sunday," South Carolina Democratic Rep. Jim Clyburn defended Democrats' response to the BuzzFeed report, including some who called for Trump's impeachment if the story proved accurate.

Reaction from House Democratic Whip James Clyburn on 'Fox News Sunday.'

"I don’t think that my Democratic friends are in any way rushing to judgment because they qualified right up front [by saying], 'If this is true,'" Clyburn argued. "When you preface your statement with 'If this is true,' that, to me, gives you all the cover you need."

Despite the brouhaha, Pence said, the White House remains focused on ending the ongoing partial federal government shutdown, now entering its 30th day.

"There's a legislative process that is going to begin on Tuesday in the United States Senate" to craft a bill implementing Trump's proposal, Pence told Wallace.

What Trump offered on Wednesday is not necessarily Trump's final offer, Pence said.

"It was disappointing to see Speaker Pelosi reject the offer before the president gave his speech" on Saturday," Pence said. "The president is offering a solution. And what we have from Democrats' leadership is just soundbites."

House Speaker Nancy Pelosi of Calif., center, speaks to reporters as she leaves an event with furloughed federal workers amid the partial government shutdown, Wednesday, Jan. 16, 2019, on Capitol Hill in Washington. (AP Photo/Andrew Harnik)

The text of a bill -- which is slated to include protections for 700,000 Deferred Action for Childhood Arrivals (DACA) recipients, $5.7 billion Trump has been seeking for a barrier along the nation's southern border with Mexico, and extended protections for 300,000 recipients of the Temporary Protected Status (TPS) program -- should be ready on Monday, Fox News has learned.

Asked whether Republicans can garner 60 votes in the Senate to defeat a possible Democratic filibuster of the bill, though, Pence was noncommittal.

"As the president often says, 'We'll see,'" Pence said, noting that Republicans have 53 votes in the chamber.

The vice president then sharply rejected suggestions by some conservative commentators, including Ann Coulter, that the plan amounted to "amnesty" -- a line of attack that suggested some Republicans in the House and Senate may not back the proposed legislation.

"This is not amnesty. There’s no pathway to citizenship, there’s no permanent status here at all, which is what amnesty contemplates," Pence told Wallace. "What this is, is a good-faith effort to address the issue."

In a series of tweets early Sunday, Trump also specifically denied that his compromise plan amounted to amnesty for illegal immigrants -- although he seemingly left open the door to offering amnesty as part of a "much bigger deal."

But Clyburn told Wallace that something more akin to a blanket, permanent protection for DACA recipients -- which some conservatives consider a form of amnesty -- might bring Democrats to the table.

"I think it's a nonstarter for him to ask for a permanent wall and for us to have a temporary fix," Clyburn said. "We want to sit down and put some stability in people's lives and have some permanent solutions to this immigration problem. And the president's team is the one who continues to play games with us."

Nevertheless, Pelosi and the Democratic leadership is needlessly prolonging the shutdown, Pence charged.

"I was sitting right next to the president [in the White House Situation Room] when speaker Pelosi said, if we re-open the government and took 30 days to negotiate, that she would not give the president funding for border security or a wall.," Pence said. "The most important thing is for the American people to let their voice be heard."

But in December, North Korea vowed that it will never unilaterally give up its nuclear weapons unless the United States removes its nuclear threat first, and U.S. intelligence officials have said the country is not denuclearizing as promised.

"The president will be announcing details in the days ahead," Pence said. "There will be a second summit. And at that summit, we'll be laying out our expectation for North Korea to take concrete steps to begin to make real the denuclearization that Kim Jong Un committed to. The president's very optimistic."

Pence concluded by extending prayers to the "four American heroes" killed in a suicide bombing Wednesday at a restaurant in Syria, inclduing two U.S. servicemembers, one Department of Defense civilian and one contractor. Another three Americans were injured in the blast.

Pressed by Wallace as to whether ISIS had truly been defeated in Syria, as Pence and Trump have repeatedly claimed, Pence said the "progress" made by the administration against ISIS has been "remarkable."

The White House, citing what the president has called an unnecessary loss of U.S. life, announced in December that the approximately 2,000 U.S. troops in Syria will depart soon.

"After President Obama withdrew American forces from Iraq in 2011, we literally saw this ISIS caliphate rise up and overrun vast areas of Syria and Iraq that had been won by the American soldiers," Pence said. "President Obama began the process of a bombing campaign two years later. But President Trump changed the rules of engagement. He told our military, his commander in chief, to go after them, and our soldiers and the Americans in the fight, along with our allies, have literally crushed the ISIS state."

Pence continued: "The president made the decision as commander-in-chief to hand off the fight against ISIS in Syria to our coalition partners. We are working, in the process of doing that. The president wants to bring our troops home, but recognize there are remnants, there are ISIS fighters still in the region. But we've taken back 99 percent of the territory that the caliphate had claimed. In a very real sense, the ISIS state has been defeated, but we will not rest or relent until we drive ISIS not only from the region, but from the face of the earth."